Does CALL instruction ALWAYS push the address pointed by EIP to stack?

Is there any condition where the return address is not pushed into stack during a function call in x86 architecture?

No. CALL will, by definition, push the return address onto the stack before jumping to the target address. That return address is EIP (or RIP) + sizeof(call instruction) (usually 5 bytes.)

Volume 2 of the Intel® 64 and IA-32 Architectures Software Developer’s Manual states that CALL:

Saves procedure linking information on the stack and branches to the called procedure specified using the target operand.

This includes:

• Near Call — "A call to a procedure in the current code segment", where EIP is pushed onto the stack.
• Far Call — "A call to a procedure located in a different segment than the current code segment", where CS, EIP are pushed onto the stack.

The alternative, not pushing a return address, is a JMP.

Every C compiler I'm familiar with will always implement function calls on x86 using a CALL instruction, with one exception: a tail call, which can be implemented with a JMP. This happens especially when one function returns the result of another function call. E.g.

int bar(int a, int b);

int foo(int a, int b)
{
    if (a < b)
       return 0;

    return bar(a, b);   // Will probably be:    jmp  bar
}